A stable ground state structure with cubic symmetry of Li3N (c-Li3N) is found by an ab initio initially symmetric random-generated crystal structure search method. Gibbs free energy, calculated within quasi-harmonic approximation, shows that c-Li3N is the ground state structure for a wide range of temperatures. The c-Li3N structure has a negative thermal expansion coefficient at temperatures lower than room temperature, mainly due to two transverse acoustic phonon modes. This c-Li3N phase is a semiconductor with an indirect band gap of 1.90 eV within hybrid density functional calculations. We also investigate the migration and energetics of native point defects in c-Li3N, including lithium and nitrogen vacancies, interstitials, and anti-site defects. Lithium interstitials are found to have a very low migration barrier (similar to 0.12 eV) and the lowest formation energy among all possible defects. The ionic conduction in c-Li3N is thus expected to occur via an interstitial mechanism, in contrast to that in the well-known alpha-Li3N phase which occurs via a vacancy mechanism.